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Parallel AI Agent Collaboration as Graph-Structured Distributed Block Optimization

Hanmin Li, Yury A. Demidovich, Peter Richtárik · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.30074 · cited by 0 works (OpenAlex) · open-access PDF

Indonesian

Retailing wall AI agen dapat menghasilkan edisi lokal yang berguna namun degradasi solusi bersama ketika edisi mereka dikombinasikan. Kami memodelkan masalah koordinasi ini sebagai pengoptimalan blok terpisah dengan tujuan yang dapat dievaluasi dengan tepat dan grafik ketergantungan yang diketahui. Set independen mengesahkan edisi yang kompatibel yang keuntungan terverifikasi, diukur terhadap solusi saat ini yang sama, menambahkan dengan tepat. Koordinator membangun kandidat yang kompatibel yang aman dan juga dapat mengevaluasi edisi interaktif untuk menangkap interaksi kendaraan yang menguntungkan. Kami membuktikan bahwa pemisahan warna publik yang optimal menghasilkan akses merger yang mempertahankan $1/χ_f(G)$ fraksi dari total perbaikan lokal yang terverifikasi, di mana $χ_f(G)$ adalah nomor kromatik yang aman dari rute. Jaminan ini di antara merger

Machine translation (Meta M2M100); the English original follows.

Abstract

Parallel AI agents can produce useful local edits yet degrade a shared solution when their edits are combined. We model this coordination problem as discrete block optimization with an exactly evaluable objective and a known dependency graph. Independent sets certify compatible edits whose verified gains, measured against the same current solution, add exactly. A coordinator constructs a safe compatible candidate and can also evaluate interacting edits to capture favorable interactions. We prove that an optimal fractional coloring yields a merger that preserves a $1/χ_f(G)$ fraction of the total verified local improvement, where $χ_f(G)$ is the graph's fractional chromatic number. This guarantee is tight among mergers that select a subset of the same proposals. Under conditional local-improvement guarantees and a block error-bound condition, repeated collaboration converges geometrically in the objective gap. The rate separates task structure, agent allocation, and computation cost, yielding a linear program for agent assignment and an explicit time-cost trade-off. Code-repair experiments show that verified merging resolves conflicts between individually useful edits that cause naive merging to fail. On larger conflict-free tasks, parallel agents reduce modeled completion time at higher input-token-equivalent cost. On three public road networks, fractional integration retains 922 units of verified graph-cut improvement across 90 paired runs. For route-search agents sharing exclusive access to vehicle routes, fractional scheduling reduces measured wall time by a median of 15% across twelve paired runs, with route-cost changes varying across runs.

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Topics: Computer science, Block (permutation group theory), Scheduling (production processes), Computation, Task (project management), Fraction (chemistry)

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